Find $\left(\frac{1+i}{\sqrt{2}}\right)^{46}$.
Solution: Not wanting to multiply out a product with 46 factors, we first see what happens when we square $(1+i)/\sqrt{2}$. We have  \[
\left(\frac{1+i}{\sqrt{2}}\right)^2 =\frac{1+2i+i^2}{(\sqrt{2})^2}= \frac{1+2i-1}{2} = i.
\] So $\left(\frac{1+i}{\sqrt{2}}\right)^{46}=\left(\left(\frac{1+i}{\sqrt{2}}\right)^2\right)^{23}=i^{23}=(i^{20})(i^3)=i^3=\boxed{-i}$.